Structured Bayesian Approximate Inference

Rasmus Bonnevie

Research output: Book/ReportPh.D. thesisResearch

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Abstract

This thesis seeks to investigate different facets of the class of Bayesian probabilistic models where the random variables exhibit strong dependencies and simultaneously lack any conditional independence structure, preventing the distribution from being factorized. Without a tractable factorization, a lot of standard inference algorithms become unavailable. We consider the application of variational inference from two different perspectives. In the first scenario we start with an extended model with conditional independence structure, and try to take the auxiliary parameters out of the equation in an optimal manner in a process emulating marginalization. In the second scenario, we tackle the variational problem directly, trying to find an efficient way to represent unfactorized models in an efficient manner, by introducing a separate form of structure to ensure efficiency. For discrete models, we find efficient approximations in the tensor literature that can model structure without sacrificing tractability. Finally, we consider a problem involving Gaussian processes that take random variables as input, leading to an inefficient inference problem. We develop a procedure that allows the stochastic component of the random input to be integrated into the kernel of the Gaussian process.
Original languageEnglish
PublisherTechnical University of Denmark
Number of pages146
Publication statusPublished - 2018
SeriesDTU Compute PHD-2018
Volume481
ISSN0909-3192

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